Date of submission – October 26, 2019
1.
Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes
$300 to profit; each Type 2 truck contributes $500. a.
Formulate an LP that will maximize Truckco’s profit.
b.
Solve the problem using Graphical approach c.
Solve the problem using Simplex algorithm
2.
One of Philip Mahn’s investments is going to mature, and he wants to determine how to invest the proceeds of $30,000. Philip is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay an 8% return.
Philip estimates the return on the stock mutual fund as 16%, 9%, or -2%, depending on whether market conditions are good, average, or poor, respectively. Philip estimates the probability of a good, average, and poor market to be 0.1, 0.85, and 0.05, respectively. a.
Construct a payoff matrix for this problem. b.
What decision should be made according to the maximax decision rule? c.
What decision should be made according to the maximin decision rule? d.
What decision should be made according to the minimax regret decision rule? e.
What decision should be made according to Herwich decision rule assuming a coefficient of optimisim of 0.8? f.
What decision should be made according to equally likelihood decision rule? g.
What decision should be made according to the EMV decision rule? h.
What decision should be made according to the EOL decision rule? i.
How much should Philip be willing to pay to obtain a market forecast that is 100% accurate?
3.
On the day of the professional football draft, the owner, general manager, and coaching staff of the New York Gladiators are attempting to decide which of the available players they should select as their pick approaches. They have three players on their big board whom they would like: Al Stonecrusher, a defensive lineman, Bruce Kowslaski, a tight end, and Charlie Speedman, a running back. They evaluate players according to four criteria — the player’s projected salary demands, speed, and size (i.e., height and weight), and the team’s position needs. Following are the group’s pairwise comparisons for the players for each of the four criteria and the pairwise comparisons for the criteria:
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Salary
A
B
C
A
B
C
Speed
Position
A
B
C
A
1
1/5
1/3
A
1
5
1/3
A
1
2
5
Size
A
B
C
A
1
¼
½
Criteria Comparison Matrix
Salary
Position
Speed
Size
Salary
1
5
3
2
Required:
B
½
1
3
B
4
1
3
B
5
1
2
B
1/5
1
1/6
Position
1/5
1
1/3
1/2
Speed
1/3
3
1
½
C
3
6
1
C
3
1/2
1
C
1/5
1/3
1
C
2
1/3
1
Size
1/2
2
2
1
Using AHP, determine which player the Gladiators should select. Check the consistency of the pairwise comparison matrix for the criteria using the random index presented hereunder.
N 2 3 4 5 6 7 8 9 10
RI 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.5
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